On Positive Solutions of Minimal Growth For Singular p-Laplacian With Potential Term
Yehuda Pinchover, Kyril Tintarev · Advanced Nonlinear Studies · 2008
Abstract Let Ω be a domain in ℝ d , d ≥ 2, and 1 < p < ∞. Fix V ∈ L ∞ loc (Ω). Consider the functional Q and its Gâteaux derivative Qʹ given by It is assumed that Q ≥ 0 on C 0 ∞ (Ω). In a previous paper [22] we discussed relations between the absence of weak coercivity of the functional Q on C 0 ∞ (Ω) and the existence of a generalized ground state. In the present paper we study further relationships between functional-analytic properties of the functional Q and properties of positive solutions of the equation Qʹ(u) = 0.